Marco Nurisso

Frankland, S. M., Marjieh, R., Nurisso, M., Fluegemann, J., Webb, T. W., Petri, G., Lewis, R. L., Cohen, J. D.

PsyArXiv

The striking constraints of some human cognitive processes stand in stark contrast to the near limitless capability of others. While we can acquire and flexibly use vast amounts of information, the amount we can process at any one time is often stiflingly limited: for example the number of items we can hold in working memory or the number of tasks that can be performed at once. Here, we integrate ideas from information theory, cognitive science, and neuroscience to offer a unified account of why processing is often so limited. We argue that this reflects a fundamental tradeoff between generalization—how effectively existing representations can be used in novel settings—and how many distinct representations can be processed in parallel. Representations that best promote strong forms of generalization — a characteristically human cognitive strength — come at the expense of surprisingly strict limits in the number of items that can be processed at once, an equally characteristic human weakness. We refer to this as the “curse of generalization.” We formulate this first in information-theoretic terms, and then in process models, including a neural network model of classic tasks used to demonstrate strict limits in human processing capacity. This tension offers a potential explanation for a range of phenomena — from performance on the tasks on which we focus, to representational learning and skill acquisition more broadly — as well as the performance of modern machine learning architectures that exhibit generalization capabilities comparable to humans.

Cognitive and NeuroAI

Guadagnuolo, F. M., Nurisso, M., Galluzzi, F., Allard, A., Petri, G.

arXiv

We establish that discrete harmonic morphisms—surjective maps maintaining harmonic functions—represent the foundational condition enabling random walks on detailed networks to project onto their simplified versions through appropriate time adjustments. We introduce the harmonic degree as a measurement tool for assessing coarse-graining quality. Testing this framework across multiple renormalization approaches, we discover that Laplacian renormalization unexpectedly achieves exact harmonic morphisms in certain networks, precisely preserving random-walk transition characteristics at particular scales. This provides methods for developing and assessing multi-scale network representations.

RUNESNetwork Foundations

Nurisso, M., Fernando, J., Deshpande, R., Perotti, A., Marjieh, R., Frankland, S. M., Lewis, R. L., Webb, T. W., Campbell, D., Vaccarino, F., Cohen, J. D., Petri, G.

ICLR

Intelligent systems must deploy internal representations that are simultaneously structured — to support broad generalization — and selective — to preserve input identity. For any model whose representational similarity between inputs decays with finite semantic resolution, we derive closed-form expressions that pin its probability of correct generalization and identification to a universal Pareto front independent of input space geometry. A minimal ReLU network trained end-to-end reproduces these laws: during learning a resolution boundary self-organizes and empirical trajectories closely follow theoretical curves. The same limits persist in two markedly more complex settings — a convolutional neural network and state-of-the-art vision-language models — confirming that finite-resolution similarity is a fundamental emergent informational constraint.

Cognitive and NeuroAIRUNES

Savietto, D., Campbell, D., Panisson, A., Nurisso, M., Petri, G., Cohen, J. D., Perotti, A.

ICML

We analyze the representational geometry of open-weight vision-language models to understand their failures in multi-object tasks such as hallucinating non-existent elements or failing to identify the most similar objects among distractions. By distilling concept vectors and validating them through steering interventions, we show that geometric overlap between these vectors strongly correlates with specific error patterns.

Cognitive and NeuroAIRUNES

Nurisso, M., Leroy, P., Petri, G., Vaccarino, F.

ICLR

Understanding the properties of the parameter space in feed-forward ReLU networks is critical for effectively analyzing and guiding training dynamics. After initialization, training under gradient flow decisively restricts the parameter space to an algebraic variety that emerges from the homogeneous nature of the ReLU activation function. In this study, we examine two key challenges associated with feed-forward ReLU networks built on general directed acyclic graph (DAG) architectures: the (dis)connectedness of the parameter space and the existence of singularities within it. We extend previous results by providing a thorough characterization of connectedness, highlighting the roles of bottleneck nodes and balance conditions associated with specific subsets of the network. Our findings clearly demonstrate that singularities are intricately connected to the topology of the underlying DAG and its induced sub-networks. We discuss the reachability of these singularities and establish a principled connection with differentiable pruning. We validate our theory with simple numerical experiments.

Topological NeuroscienceCognitive and NeuroAI

Nurisso, M., Morandini, M., Lucas, M., Vaccarino, F., Gili, T., Petri, G.

Nature Physics

We propose a cross-order Laplacian renormalization group (X-LRG) scheme for arbitrary higher-order networks. The renormalization group is a pillar of the theory of scaling, scale-invariance, and universality in physics. An RG scheme based on diffusion dynamics was recently introduced for complex networks with dyadic interactions. Despite mounting evidence of the importance of polyadic interactions, we still lack a general RG scheme for higher-order networks. Our approach uses a diffusion process to group nodes or simplices, where information can flow between nodes and between simplices (higher-order interactions). This approach allows us (i) to probe higher-order structures, defining scale-invariance at various orders, and (ii) to propose a coarse-graining scheme. We demonstrate our approach on controlled synthetic higher-order systems and then use it to detect the presence of order-specific scale-invariant profiles of real-world complex systems from multiple domains.

Network Foundations

Santoro, A., Nurisso, M., Petri, G.

EUSIPCO

We propose edge-based Laplacian operators for processing brain signals, moving beyond traditional node-centric approaches to capture higher-order topological features of brain functional data.

Topological NeuroscienceNetwork FoundationsRUNES

Nurisso, M., Arnaudon, A., Lucas, M., Peach, R. L., Expert, P., Vaccarino, F., Petri, G.

Chaos: An Interdisciplinary Journal of Nonlinear Science

Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three main groups: simple models, Hodge-coupled models, and order-coupled (Dirac) models. Our framework is based on topology, discrete differential geometry as well as gradient flows and frustrations, and permits a systematic analysis of their properties. We establish an equivalence between the simple simplicial Kuramoto model and the standard Kuramoto model on pairwise networks under the condition of manifoldness of the simplicial complex. Then, starting from simple models, we describe the notion of simplicial synchronization and derive bounds on the coupling strength necessary or sufficient for achieving it. For some variants, we generalize these results and provide new ones, such as the controllability of equilibrium solutions. Finally, we explore a potential application in the reconstruction of brain functional connectivity from structural connectomes and find that simple edge-based Kuramoto models perform competitively or even outperform complex extensions of node-based models.

Network Foundations

Azeglio, S., Poetto, S., Savant, L., Nurisso, M.

Computational models of vision have traditionally been developed in a bottom-up fashion, by hierarchically composing a series of straightforward operations - i.e. convolution and pooling - with the aim of emulating simple and complex cells in the visual cortex, resulting in the introduction of deep convolutional neural networks (CNNs). Nevertheless, data obtained with recent neuronal recording techniques support that the nature of the computations carried out in the ventral visual stream is not completely captured by current deep CNN models. To fill the gap between the ventral visual stream and deep models, several benchmarks have been designed and organized into the Brain-Score platform, granting a way to perform multi-layer (V1, V2, V4, IT) and behavioral comparisons between the two counterparts. In our work, we aim to shift the focus on architectures that take into account lateral recurrent connections, a ubiquitous feature of the ventral visual stream, to devise adaptive receptive fields. Through recurrent connections, the input s long-range spatial dependencies can be captured in a local multi-step fashion and, as introduced with Gated Recurrent CNNs (GRCNN), the unbounded expansion of the neuron s receptive fields can be modulated through the use of gates. In order to increase the robustness of our approach and the biological fidelity of the activations, we employ specific data augmentation techniques in line with several of the scoring benchmarks. Enforcing some form of invariance, through heuristics, was found to be beneficial for better neural predictivity.

Cognitive and NeuroAI